Question

the equation $d = \frac{13}{v}$ shows that the density of a particular substance equals a mass of 13 grams divided by the volume of the substance. what happens to the density as the volume approaches 0?\
the density approaches 1.\
the density approaches infinity.\
the density approaches 13\
the density approaches 0.

Explanation:

Step1: Analyze the function

The density function is \( D = \frac{13}{V} \), where \( V \) is the volume. We need to see the behavior of \( D \) as \( V \to 0 \).

Step2: Consider the limit

As \( V \) approaches 0 (from the positive side, since volume can't be negative in this context), the denominator of the fraction \( \frac{13}{V} \) gets smaller and smaller. When we divide a constant (13) by a number that is getting closer and closer to 0, the result gets larger and larger, approaching infinity. For example, if \( V = 0.1 \), \( D = 130 \); if \( V = 0.01 \), \( D = 1300 \); as \( V \) gets closer to 0, \( D \) becomes extremely large, approaching infinity.

Answer:

The density approaches infinity.